Course Code

P455

Credit

8

Prerequisite

P302 (Statistical Mechanics)

Total Hours

42 Lectures + 14 Tutorials

Outcome of the Course

This course teaches the students advanced concepts and methods in statistical mechanics crucial for the student to take up basic research work.

Approval

Syllabus

- Introduction to critical phenomena and first order phase transition. Survey of experimental results and scaling hypothesis, introduction to critical exponents and universality.
- Review of thermodynamic potentials, introduction to order parameter and response functions.
- Introduction to interacting systems: study of one dimensional Ising model via transfer matrix, lack of phase transition in one dimension, study of Ising model in two dimensions, XY and Heisenberg model.
- Mean field theory: calculation of order parameter, response functions and correlation functions using Curie-Weiss mean field theory and Landau-Ginzberg theory, calculation of critical exponents for mean field systems, range of validity of mean field theory.
- Introduction to re-normalization group (RG): Kadanoff block spins and real space RG methods, Perturbative RG in momentum space: Wilson-Fisher RG and epsilon expansion, broken continuous symmetry: Mermin Wagner theorem, Goldstone modes and Kosterlitz Thouless phase transition, introduction to non-linear sigma models, quantum critical phenomena and quantum phase transitions, introduction to 1D Transverse Field Ising Model and introduction to Bose- Hubbard model.

Reference Books

- Introduction to phase Transitions and Critical phenomena by H. Eugene Stanley
- Modern approach to Critical phenomena by Igor Herbut
- Statistical physics: Statics, Dynamics and Renormalization by Leo p. Kadanoff
- The Theory of Critical phenomena by J. J. Binney, a. J. Fisher, M. E. J. newman
- Modern Theory of Critical phenomena by Shang-keng Ma
- Statistical Mechanics of phase Transitions by J. Yeomans
- Field Theory, the Renormalisation group and Critical phenomena by Daniel J. Amit